This mini-Workshop will be held on Thursday, January 18th, 2018
- Benoît Daniel: Minimal isometric immersions
Abstract: A classical result in geometry of submanifolds states that every simply connected minimal surface in R^3 belongs to a one-parameter family of minimal surfaces that are isometric (intrinsically) to it, called the associate family, and that, conversely, two isometric minimal surfaces are isometric. We will study a generalisation of these results when the ambient space is a product manifold S^2 x R or H^2 x R (where S^2 and H^2 are, respectively, the sphere and the hyperbolic plane), relating this problem to the study of a system of two partial differential equations.
- Louis Merlin: Convex-cocompact locally symmetric manifolds and their deformations
Abstract: We first describe a possible definition of a convex-cocompact manifold modeled on an arbitrary symmetric space, following the proposition of Kapovich, Leeb and Porti using Morse actions. We then present a first attempt to understand their deformations spaces.
- Alexander Thomas: Parabolic gauge reduction of connexions on surfaces
Abstract: A famous result of Atiyah and Bott asserts that the gauge group action on the space of conexions on a surface is hamiltonian with moment map the curvature. Restricting this action to a parabolic subgroup gives an interesting space which we will investigate. This space is linked to solutions of ordinary differential equations and carries a symplectic structure. Joint work with Vladimir Fock.